1. Field of the invention
The invention is concerned with wireless communications apparatus, and particularly with wireless communications apparatus employing preceding and/or beamforming.
2. Discussion of Background
MIMO communications equipment can use beamforming techniques to improve efficacy of communication. Beamforming uses interference effects at multiple antennas such that the superimposed signals at the individual antennas give rise to a directional beam, or a beam of desired profile given operating conditions.
In systems employing precoding or beamforming, channel knowledge is used at the transmitter in order to enhance the link quality. In an OFDM system, a preceding matrix is applied to each individual subcarrier. The matrix governs the weights allocated to each spatial channel, to cause formation of a desired beam profile. The optimal weights are found from the singular value decomposition (SVD) of the channel. This is described in “Limited feedback precoding for spatial multiplexing systems” (D. J. Love and R. W. Heath, Jr, Globecom 2003, pp 1857-1861). In an OFDM system, the SVD needs to be computed on every subcarrier, which may be costly.
There are several available techniques for computation of the SVD. Hessenberg decomposition, described in “Linear algebra and its applications” (G. Strang, Harcourt-Brace-Jovanovich, 3rd ed., 1986), Hestenes method described in “Inversion of matrices by biorthogonalization and related results” (M. Hestenes, Journal of the Society for Industrial and Applied Mathematics, vol 6, no 1, pp 51-90, March 1958), and different types of eigenvalue decomposition (again, Strang, referenced above), are commonly employed.